You've recently moved to Florida which leads me to concur with Crankin. Every time I've moved I've had problems for a couple of seasons as my asthma adjusted to the new environment/pollen mix/ etc. The allergist may be able to help you more quickly, it's worth checking out. I don't have "normal" asthma, but what they call a "cough variant" form, though I do wheeze - but after a certain point the coughing reaches pretty extreme levels for me.

I really hope it turns out to be more pollen related than a mold issue, crossing my fingers for you!